Abstract

Discrete-time sliding mode controllers that utilize saturation-based reaching laws require a gain that ensures contraction within the boundary layer in the presence of multiplicative gain uncertainty. The conventional fixed-gain approach does not maintain this property at moderate uncertainty levels. This work introduces a family of admissible reaching gains and identifies a unique optimal gain that guarantees a specified worst-case contraction. The proposed method offers a closed-form solution to the worst-case contraction problem over the gain-uncertainty interval and determines the optimal contraction factor for the saturation-based reaching law for any finite uncertainty ratio. The optimal gain is integrated into a discrete-time integral sliding-mode framework, thereby eliminating the reaching phase. Furthermore, a past-step disturbance estimator with a confidence factor is introduced to prevent error amplification, which reduces the quasi-sliding band from first to second order in the sampling period when the realized gain approximates its nominal value. The effectiveness of the proposed approach is validated through its application to a photovoltaic battery-charging system with a DC–DC boost converter, achieving robust inductor-current regulation across three battery banks under varying irradiance conditions in a switching-level model with parasitic elements.

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